Lepidus is one of Shakespeare's most carefully drawn peripheral characters — always present, never central. He was the third triumvir of the real Roman world, brought in by Antony and Caesar as a useful ally with forces to contribute and a famous name. But from the beginning, his role in Shakespeare's play is to smooth things over and be managed. Here, even the departure logistics place him last — he takes the longer route while the others 'win two days' on him. It's a small detail that encapsulates his position perfectly. He will shortly be eliminated from the triumvirate by Caesar, who annexes his territories. The servants in 2.7 will observe his drunkenness with a kind of contemptuous pity. Shakespeare gives him dignity but no weight.

This is a structural 'bridge' scene — a brief passage of no dramatic weight that moves characters and the audience from one location to another. Shakespeare uses these constantly in his history plays and political tragedies. They serve several functions: they keep the geography of the world alive; they let the audience absorb what just happened before the next major scene; and they signal that the world of the play continues moving even when we're not watching the main characters. In a play as sprawling as Antony and Cleopatra — which covers the entire Mediterranean world — these transitional scenes are especially necessary. They remind the audience that this is a world in motion, not just a series of tableau confrontations.